Final answer:
The musician who preferred to play only his original compositions and was associated with the advent of bebop is Thelonious Monk. His music embodied the modernist spirit of breaking from tradition, a theme that resonated with figures like Schoenberg in classical music and paralleled the cultural shifts of the hipsters and Beat Generation.
Step-by-step explanation:
The musician associated with the advent of bebop who defined convention by preferring to play only his original compositions was Thelonious Monk. Monk's approach to jazz fits into the broader context of modernist musical experimentation where figures like W.C. Handy, Arnold Schoenberg, and Igor Stravinsky pushed beyond the traditional boundaries of music. Bebop itself was a reaction against big band music and featured complex improvisations, innovative rhythms, and a departure from popular melodies of the time.
Bebop represented the highs and lows of life in black enclaves like New Orleans and transformed jazz into an up-tempo experience with bolder rhythm and harmony. As a part of this musical evolution, Monk's own compositions were steeped in bebop's idiosyncrasies, making use of dissonance, unexpected turns in melody, and rhythmic complexity. This was similar to how Schoenberg's atonality and twelve-tone scale represented a departure from the expected Western musical scales, echoing the modernist desire to challenge and redefine the norms of the day.
Jazz culture itself, which had a profound influence on the so-called 'hipsters' and the Beat Generation, reached a turning point with bebop in the 1940s, signifying a shift in the subcultural landscape that extended well into the 1950s. Thelonious Monk's emphasis on original compositions during this period marked him as a truly innovative force in music and an integral part of the bebop revolution.